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Reset stabilisation of positive linear systems. (English) Zbl 1347.93215
Summary: In this paper, the problems of reset stabilization for Positive Linear Systems (PLSs) are investigated. Some properties relating to reset control of PLSs are first revealed. It is shown that these properties are different from the corresponding ones of general linear systems. Second, a class of periodic reset scheme is designed to exponentially stabilize an unstable PLS with a prescribed decay rate. Then, for a given PLS with reset control, some discussions on the upper bound of its decay rate are presented. Meanwhile, the reset stabilization for PLSs in a special case is probed as well. Finally, two numerical examples are used to demonstrate the correctness and effectiveness of the obtained theoretical results.

MSC:
93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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